The grades of a freshman college class, obtained after the first year of college, were analyzed. Seventy percent of the students in the top quarter of the college class had graduated in the upper 10% of their high school class, as had 50% of the students in the middle half of the college class and 20% of the students in the bottom quarter of the college class.a. What is the probability that a randomly chosen freshman graduated in the upper 10% of his high school class?b. What is the probability that a randomly chosen freshman who graduated in the upper 10% of the high school class will be in the top quarter of the college class?c. What is the probability that a randomly chosen freshman who did not graduate in the upper 10% of the high school class will not be in the top quarter of the college class?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The grades of a freshman college class, obtained after the first year of college, were analyzed. Seventy percent of the students in the top quarter of the college class had graduated in the upper 10% of their high school class, as had 50% of the students in the middle half of the college class and 20% of the students in the bottom quarter of the college class.
a. What is the
b. What is the probability that a randomly chosen freshman who graduated in the upper 10% of the high school class will be in the top quarter of the college class?
c. What is the probability that a randomly chosen freshman who did not graduate in the upper 10% of the high school class will not be in the top quarter of the college class?
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